Tutorial suggestion

[Almi]

Dear deal.II developers,

Thank you very much for the excellent job in creating very powerful product. I find it amazing that you guys offer it in open source.

I think that it would make your code even more helpful if the step 3 of your great tutorial would be extended. Very often in Physics one has to solve the generalized Poisson equation:

grad [ e(r) * grad[V(r)] ] = - f(r)

In practice this problem is usually defined on a complex geometry, which contains multiple metal electrodes (boundary conditions), dielectric layers e(r), and some charge distribution f(r). For example, it is interesting to calculate electrostatic potential V(r) inside and around two metal plates with fixed potential, which are separated by dielectric layer of thickness d. This is a finite capacitor problem.

In deal.II not-that-trivial triangulation has to be constructed. In 2d that would be a large rectangle with two rectangular "holes", which will represent the metal plates. Then boundary conditions will be defined as follows: zero on the large rectangle and some potential on the metal plates. I guess this can be achieved using GridGenerator::merge_triangulations() method.

From my own experience I can tell that it is not so easy to find an example of solution of the generalized Poisson equation using finite element method. I believe that it would be interesting to many folks out there. Ultimately that would make the learning curve of deal.II less steep and will promote the software even further.

What do you think?

[Timo Heister]

Dear Alexander,

thanks for your suggestions. It sounds like that you are looking for a
solution of a problem you are working on right now?

Each tutorial steps we have tries to focus on demonstrating a single,
small feature set. The idea is that a user looking on how to do a
certain thing (for example, how to generate a mesh) can find exactly
that. So it is unlikely to find a step that does everything you might
need.

We already have several problems solving the Poisson equation for
example (step-4, ...). But, I agree with you that complex geometries
are difficult to do. I am working on a tutorial for that.

If you have specific questions, please let us know.

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--
Timo Heister
http://www.math.tamu.edu/~heister/

[Wolfgang Bangerth]

> I think that it would make your code even more helpful if the step 3 of your
> great tutorial would be extended. Very often in Physics one has to solve the
> generalized Poisson equation:
>

> grad [ e(*r*) * grad[V(*r*)] ] = - f(*r*)

This equation is solved in steps 5 and 6, for example. But it's true that
using complex geometries aren't well described in the tutorial. Timo had a
plan to add a tutorial program on this for a while already, as he mentioned in
the other email.

Best
W.

--
------------------------------------------------------------------------
Wolfgang Bangerth email: bang...@math.tamu.edu
www: http://www.math.tamu.edu/~bangerth/

[Almi]

Dear Timo and Wolfgang,

Thank you very much for your replays.

I think that your tutorials are fantastic. In fact this is a reason of my interest for deall.ii in the first place. I am looking forward to read your tutorial on complex geometries.

Indeed, by looking through the tutorial pages one may find figure out how to solve the generalized Poisson equation. I agree that it is unreasonable to show how to solve every little problem here. I was trying to make a point that the problem, which I described occurs quite often in Physics.  I have not found any well documented solver of this problem as a whole using c++. Surely, deal.II would get more users when such a tutorial would be present. Perhaps you guys could use the generalized Poisson equation as an example for the planned tutorial on complex geometry problem.

Thank you for your effort and time!

Best regards,
Alex.

[Wolfgang Bangerth]

> Indeed, by looking through the tutorial pages one may find figure out how to
> solve the generalized Poisson equation. I agree that it is unreasonable to
> show how to solve every little problem here. I was trying to make a point that
> the problem, which I described occurs quite often in Physics. I have not
> found any well documented solver of this problem as a whole using c++. Surely,
> deal.II would get more users when such a tutorial would be present. Perhaps
> you guys could use the generalized Poisson equation as an example for the
> planned tutorial on complex geometry problem.

Tutorial programs are, on purpose, restricted to individual topics. To build
your own application, you typically have to take pieces from several programs
(e.g. the spatially variable coefficient from step-5, complex meshes from
Timo's future program, a linear solver from somewhere else, etc).

That said, step-5 did not explain well the equation we are solving here. I am
adding a few sentences to the introduction to this end.

[Almi]

Thank you Wolfgang.